IJPAM: Volume 73, No. 2 (2011)

Abstract. The aim of this paper is to explore the concept of observability
with constraints of the gradient for distributed parabolic system
evolving in spatial domain . It consists in the
reconstruction of the initial state gradient and must be between
two prescribed functions in a subregion of . We
give definitions and some properties of this kind of regional
observability and we describe two approaches to solve this problem
where the first is based on subdifferential techniques and the
second uses the lagrangian multiplier method. This last approach
leads to an algorithm which is performed by example and
simulation.